Sounds like your clutch pedal linkage (under the dash) is too tight, as Mattback said. I will venture to guess that your clutch pedal has zero play. Am I right? Let me explain...

What is probably happening is that the pressure in the clutch line is never completely released, because the pedal linkage is always pushing in on the master cylinder. This will hold the clutch in a semi-engaged position. Being semi engaged (and probably slipping minutely) will cause it to over heat and become slippery. The 20 minutes part is what tells me that it is heat build up that is causing this. This is also very bad for your throw out bearing. Shorten the rod connecting the master cylinder and pedal. You may also have to adjust the bumper that the pedal rests against normally.